Indeed, for a suitable choice of the amplitude \(\mathcal {R}\) , the BEC probability density
\(\rho ^{(B)}\sim |\mathcal {R}|^2\)  is shown to mimic the energy density of a classical dust-like
matter, presumably the cold dark matter (CDM), whereas the potential \(U_{_Q}\)  is
positive (repulsive) and even a constant, that acts as a cosmological constant
dark energy (DE) component \(\Lambda \) , albeit of a quantum origin
[1]}, [2]}.
However, from a rather general perspective, such a CDM mimicry of \(\rho ^{(B)}\)  may only
be partial, since the potential \(U_{_Q}\)  may evolve dynamically and contribute to the
CDM as well. That is to say, \(\rho ^{(B)}\)  or \(U_{_Q}\)  may not individually be responsible,
in general, for shaping up the course of evolution of only the CDM or only the DE.
Instead, their combined effect may be looked upon as what leads to some specific
evolution profile of the entire cosmological dark sector. Strikingly however,
one may still reckon the constancy of the effective DE component, and that the
CDM effectively results from a close interplay of not only the evolving \(\rho ^{(B)}\) 
and \(U_{_Q}\) , but also the density of the visible (baryonic) matter content of the
universe. While demonstrating all these in this paper, we shall endeavor to make
it clear that the formalism developed herein differs substantially from the
plethora of proposals encompassing the ways to treat the BEC as a plausible CDM
candidate in the literature
[3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}.
In particular, it is worth noting here that, to the best of our knowledge,
neither the quantum effects of the BEC on the background level cosmic
evolution, nor the possibility of a BEC accounting for the whole dark sector,
has been explored with rigour.
